This is a check of the ENSO model by back-extrapolating against the Unified ENSO Proxy (UEP) records. The UE proxy is averaged together from various data sets and only has a resolution of one year, with a distinct possibility that the absolute yearly alignment could be off. The alignment is easy to determine for the modern instrumental era as one can calibrate against SOI and NINO data, but for coral proxy data before 1880, the calibration becomes more difficult to verify. This is important because a tidal forcing model is critically dependent on keeping absolute orbital phase relationships over all times. According to the recurring alignment of eclipses this period can be checked only after 372 years [1]. The UEP goes back to 1650, providing a the time series about 330 years long, so not long enough to detect a repeat pattern in the ENSO behavior.
With that said, the pre-1880 ENSO behavior can be captured effectively by slightly relaxing the fit to the SOI data that the model was initially based on. In the multi-panel figure below, the last panel features monthly data (after 1880 with the modern-era SOI fit) and all others are yearly (from 1650 to 1880).
So the temporal lunisolar forcing pattern was essentially the same before and after 1880, but a slight temporal shift (at least partly due to the yearly to month transition) and an independent spatial scaling (impacting the amplitude) was applied prior to 1880. Recall that only three lunar periods are involved in the fit, along with the annual harmonics. From 1650 to 1880 the correlation coefficient is 0.80
Before ~1900, the variance of the UEP appears to be significantly reduced as shown below. This indicates the possibility that the standing wave boundary conditions changed around that time. The stationary model of ENSO has a more stable variance over the 300 year time span than found from the coral proxy data, so we are forced to parameterize the model into two separate intervals.
References
[1] J. N. Stockwell, “On the law of recurrence of eclipses on the same day of the tropical year,” The Astronomical Journal, vol. 15, pp. 73–75, 1895.
GeoEnergy Math 
The salient point is that trying to fit a curve as chaotic-appearing as an ENSO time-series with just 4 sinusoidal waves is difficult enough. But then to extend that to almost double the length — from 135 years to an additional 230 years with what are essentially minor tweaks to the boundary conditions — is next to impossible if it was a truly chaotic behavior.
If there was one curious aspect to deal with, it’s that the magnitude of ENSO excursions appear to increase by a factor of 2 between 1880 and 1900. The Krakatoa volcano erupted in 1883. It is located 6 degrees south of the equator and produced an “equatorial smoke stream” visible from the ground. It actually changed the local geography. Could that have changed the equatorial boundary conditions slightly?
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As far as Krakatoa impacting the spatial boundary conditions of a Pacific ocean dipole, think in terms of the flow through a narrowed straight. This paper The Indonesian throughflow, its variability and centennial change describes the idea. Krakatoa is famously in the straight East of Java but the blockage can be visualized here:
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Oceanography Surrounding
Krakatau Volcano
in the Sunda Strait, Indonesia
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This paper shows a strong biennial component in their proxy, even though they dont call attention to it
Ukhvatkina, Olga N., Alexander M. Omelko, Alexander A. Zhmerenetsky, and Tatyana Y. Petrenko. “Autumn–winter Minimum Temperature Changes in the Southern Sikhote-Alin Mountain Range of Northeastern Asia since 1529 AD.” Climate of the Past 14, no. 1 (January 16, 2018): 57–71. https://doi.org/10.5194/cp-14-57-2018.
Click to access cp-14-57-2018.pdf
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Difficult enough to fit modern instrumental record of ENSO to 4 established and necessary frequencies (1 solar, 2 lunar, 1 lunisolar), but then when it easily extends to another 230 years of coral proxy records dating back to 1650, the model becomes essentially validated.
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This is an overfit to the 1650-1880 UEP proxy data. It reaches a correlation coefficient of over 0.9 on this interval, yet the extrapolated model over the modern era still lays fairly cleanly on top of the NINO34 data
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The amazing sinSin transform derived from solving Navier-Stokes.
Initial ENSO fit to instrument data is lower figure.
Upper is proxy fit — remarkably similar
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